Systems and Methods for Short Media Defect Detection Using Non-Binary Coded Information

ABSTRACT

Various embodiments of the present invention provide systems and methods for media defect detection.

BACKGROUND OF THE INVENTION

The present inventions are related to systems and methods fortransferring information, and more particularly to systems and methodsfor determining problems related to a medium associated with a datatransfer.

Various data transfer systems have been developed including storagesystems, cellular telephone systems, radio transmission systems. In eachof the systems data is transferred from a sender to a receiver via somemedium. For example, in a storage system, data is sent from a sender(i.e., a write function) to a receiver (i.e., a read function) via astorage medium. The effectiveness of any transfer is impacted by anydefects associated with the transfer medium. In some cases, data losscaused by defects in the transfer medium can make recovery of data fromthe transfer medium difficult even for data received from non-defectiveareas or times. Various approaches have been developed for identifyingdefects in the transfer medium. Such approaches provide a generalability to identify defects, but in many cases are inaccurate. In thebest case, this inaccuracy limits the effectiveness of any defectidentification. In the worst case, inaccurate defect detection mayactually hamper the data recovery process. The inability to detect shortmedia defects is increased where non-binary symbols are being decoded assuch symbols do not exhibit independence between adjacent bits.

Hence, for at least the aforementioned reasons, there exists a need inthe art for advanced systems and methods for defect detection.

BRIEF SUMMARY OF THE INVENTION

The present inventions are related to systems and methods fortransferring information, and more particularly to systems and methodsfor determining problems related to a medium associated with a datatransfer.

Various embodiments of the present invention provide data processingsystems that include: a data detector circuit, a defect detectorcircuit, and a data decoder circuit. The data detector circuit isoperable to apply a data detection algorithm to a symbol based data setguided by a decoded output to yield a symbol based detected output. Thedefect detector circuit includes: a data pre-processing circuit and abinary data detection circuit. The data pre-processing circuit isoperable to pre-process the symbol based detected output to yield apre-processed output, and the binary data detection circuit is operableto provide a defect indicator corresponding to a probable defectidentified based on the pre-processed output. The data decoder circuitis operable to apply a data decode algorithm to a decoder input derivedfrom the detected output modified based on the defect indicator toupdate the decoded output.

In some instances of the aforementioned embodiments, the symbol baseddata set is a series of multi-bit symbols. In some such cases, themulti-bit symbols are two bit symbols. In some of the aforementionedinstances, the data pre-processing circuit is further operable to:calculate an input value based upon a combination of the detected outputand the decoded output; and compare the input value with a thresholdvalue. In some cases, the threshold value is programmable.

In various instances of the aforementioned embodiments, the input valueis calculated in accordance with the following equation:

${m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}},$

where i, j indicate a particular element of one of the series ofmulti-bit symbols, where ei, ej indicate a particular element of the oneof the series of multi-bit symbols, where ai, aj indicate a particularelement of the one of the series of multi-bit symbols, where Sa_(i,j)represents a soft data element of the detected output, where Sa_(ai,aj)represents a soft data element of the detected output, whereinrepresents a soft data element of the decoded output, where Se_(ei,ej)represents a soft data element of the decoded output, and where Se_(i,j)represents a soft data element of the decoded output.

In one or more instances of the aforementioned embodiments, thepre-processed output is calculated in accordance with the followingequation:

[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)],

where the input value is greater than the threshold; and

[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei)′,(−1)^(ej)′],

where the input value is less than the threshold. In the aforementioned,ei, ej indicate a particular element of one of the series of multi-bitsymbols, ei′, ej′ indicate a particular element of the one of the seriesof multi-bit symbols, and ai, aj indicate a particular element of theone of the series of multi-bit symbols.

This summary provides only a general outline of some embodiments of theinvention. Many other objects, features, advantages and otherembodiments of the invention will become more fully apparent from thefollowing detailed description, the appended claims and the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the various embodiments of the presentinvention may be realized by reference to the figures which aredescribed in remaining portions of the specification. In the figures,like reference numerals are used throughout several figures to refer tosimilar components. In some instances, a sub-label consisting of a lowercase letter is associated with a reference numeral to denote one ofmultiple similar components. When reference is made to a referencenumeral without specification to an existing sub-label, it is intendedto refer to all such multiple similar components.

FIG. 1 shows a storage system including a read channel with a shortdefect detector circuit in accordance with various embodiments of thepresent invention;

FIG. 2 depicts a data processing circuit including a short defectdetector circuit in accordance with various embodiments of the presentinvention;

FIG. 3 is a flow diagram showing a method in accordance with someembodiments of the present invention for data processing including shortmedia defect detection;

FIG. 4 shows another data processing circuit including a short defectdetector circuit in accordance with various embodiments of the presentinvention; and

FIGS. 5 a-5 b are flow diagrams showing a method in accordance with oneor more embodiments of the present invention for data processingincluding short media defect detection.

DETAILED DESCRIPTION OF THE INVENTION

The present inventions are related to systems and methods fortransferring information, and more particularly to systems and methodsfor determining problems related to a medium associated with a datatransfer.

Various embodiments of the present invention provide for data processingsystems that include media defect detection circuitry. The media defectdetection circuitry is capable of detecting short media defects (e.g.,defects less than thirty-two bits). In some cases, the data beingprocessed is non-binary and the media defect detection circuitry istailored for such non-binary data where the successive bits in aprocessing data input are not independent. The defect detection circuitutilizes an existing media defect detector circuit modified to include adata pre-processing circuit that pre-processes a data input prior tointroducing the pre-processed data to the media defect detector circuit.

Turning to FIG. 1, a storage system 100 including a read channel circuit110 having a short media defect detector circuit is shown in accordancewith various embodiments of the present invention. Storage system 100may be, for example, a hard disk drive. Storage system 100 also includesa preamplifier 170, an interface controller 120, a hard disk controller166, a motor controller 168, a spindle motor 172, a disk platter 178,and a read/write head 176. Interface controller 120 controls addressingand timing of data to/from disk platter 178. The data on disk platter178 consists of groups of magnetic signals that may be detected byread/write head assembly 176 when the assembly is properly positionedover disk platter 178. In one embodiment, disk platter 178 includesmagnetic signals recorded in accordance with either a longitudinal or aperpendicular recording scheme.

In operation, read/write head assembly 176 is accurately positioned bymotor controller 168 over a desired data track on disk platter 178.Motor controller 168 both positions read/write head assembly 176 inrelation to disk platter 178 and drives spindle motor 172 by movingread/write head assembly to the proper data track on disk platter 178under the direction of hard disk controller 166. Spindle motor 172 spinsdisk platter 178 at a determined spin rate (RPMs). Once read/write headassembly 176 is positioned adjacent the proper data track, magneticsignals representing data on disk platter 178 are sensed by read/writehead assembly 176 as disk platter 178 is rotated by spindle motor 172.The sensed magnetic signals are provided as a continuous, minute analogsignal representative of the magnetic data on disk platter 178. Thisminute analog signal is transferred from read/write head assembly 176 toread channel circuit 110 via preamplifier 170. Preamplifier 170 isoperable to amplify the minute analog signals accessed from disk platter178. In turn, read channel circuit 110 decodes and digitizes thereceived analog signal to recreate the information originally written todisk platter 178. This data is provided as read data 103.

As part of processing data accessed from disk platter 178, read channelcircuit 110 performs a media defect detection process operable todetermine whether received data is associated with a defective region ofdisk platter 178. This media defect detection includes pre-processing adetected output from a data detector circuit, and subsequentlydetermining a media defect based upon a combination of the pre-processeddata and a decoded output from a data decoder circuit. When a mediadefect is detected, soft data corresponding to the location of thedetected media defects are scaled to reduce the impact of the mediadefect. In some embodiments of the present invention, the dataprocessing circuit including the short media defect detector circuit maybe implemented similar to that discussed below in relation to FIG. 2 orFIG. 4, and/or may apply data processing similar to that discussed belowin relation to FIG. 3 or FIGS. 5 a-5 b.

It should be noted that storage system 100 may be integrated into alarger storage system such as, for example, a RAID (redundant array ofinexpensive disks or redundant array of independent disks) based storagesystem. Such a RAID storage system increases stability and reliabilitythrough redundancy, combining multiple disks as a logical unit. Data maybe spread across a number of disks included in the RAID storage systemaccording to a variety of algorithms and accessed by an operating systemas if it were a single disk. For example, data may be mirrored tomultiple disks in the RAID storage system, or may be sliced anddistributed across multiple disks in a number of techniques. If a smallnumber of disks in the RAID storage system fail or become unavailable,error correction techniques may be used to recreate the missing databased on the remaining portions of the data from the other disks in theRAID storage system. The disks in the RAID storage system may be, butare not limited to, individual storage systems such as storage system100, and may be located in close proximity to each other or distributedmore widely for increased security. In a write operation, write data isprovided to a controller, which stores the write data across the disks,for example by mirroring or by striping the write data. In a readoperation, the controller retrieves the data from the disks. Thecontroller then yields the resulting read data as if the RAID storagesystem were a single disk.

A data decoder circuit used in relation to read channel circuit 110 maybe, but is not limited to, a low density parity check (LDPC) decodercircuit as are known in the art. Such low density parity checktechnology is applicable to transmission of information over virtuallyany channel or storage of information on virtually any media.Transmission applications include, but are not limited to, opticalfiber, radio frequency channels, wired or wireless local area networks,digital subscriber line technologies, wireless cellular, Ethernet overany medium such as copper or optical fiber, cable channels such as cabletelevision, and Earth-satellite communications. Storage applicationsinclude, but are not limited to, hard disk drives, compact disks,digital video disks, magnetic tapes and memory devices such as DRAM,NAND flash, NOR flash, other non-volatile memories and solid statedrives.

Turning to FIG. 2 depicts a data processing circuit 200 including ashort defect detector circuit 250 in accordance with various embodimentsof the present invention. Data processing circuit 200 includes a datadetector circuit 210 that applies a data detection algorithm to a datainput 201 guided by a soft decoded output (La) 232. In some embodimentsof the present invention, data input 201 is derived from a storagemedium. Based upon the disclosure provided herein, one of ordinary skillin the art will recognize a variety of sources for data input 201. Datadetector circuit 210 may be, but is not limited to, a maximum aposteriori data detector circuit, or a Viterbi algorithm data detectorcircuit. Of note, the general phrases “Viterbi data detection algorithm”or “Viterbi algorithm data detector circuit” are used in their broadestsense to mean any Viterbi detection algorithm or Viterbi algorithmdetector circuit or variations thereof including, but not limited to,bi-direction Viterbi detection algorithm or bi-direction Viterbialgorithm detector circuit. Also, the general phrases “maximum aposteriori data detection algorithm” or “maximum a posteriori datadetector circuit” are used in their broadest sense to mean any maximum aposteriori detection algorithm or detector circuit or variations thereofincluding, but not limited to, simplified maximum a posteriori datadetection algorithm and a max-log maximum a posteriori data detectionalgorithm, or corresponding detector circuits. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of data detector circuits that may be used in relation todifferent embodiments of the present invention. Application of the datadetection algorithm by data detector circuit 210 yields a detectedoutput (Le) 211.

Detected output 211 and soft decoded output 232 are provided to a datapre-processing circuit 260 that is operable to modify a symbol basedinformation set into a binary based information set. In particular, apivot value (m) is computed in accordance with the following equation:

${m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}},$

where i, j indicate a particular element of a given symbol. For two bitsymbols, i goes from 0 to 1 and j goes from 0 to 1. It should be notedthat while this embodiment is described in relation to two bit symbolsthat it may be used in relation to symbols with three or more bits. Forthe case of two bit symbols, “Sa” represents a soft data element ofdetected output (La) 211, and “Se” represents a soft data element ofsoft decoded output (Le) 232, and detected output (La) 211 and softdecoded output (Le) 232 are defined as follow:

La=[Soft Data_(—) a ₀₀,Soft Data_(—) a ₀₁,Soft Data_(—) a ₁₀,SoftData_(—) a ₁₁]; and

Le=[Soft Data_(—) e ₀₀,Soft Data_(—) e ₀₁,Soft Data_(—) e ₁₀,SoftData_(—) e ₁₁].

In some cases, Soft Data_a_(i,j) and Soft Data_e_(i,j) are loglikelihood ratio (LLR) data. In such a case, the hard decision of eachsymbol of detected output (La) 211 and the hard decision of each symbolof decoded output (Le) 232 are described as follows:

Hard Decision La={ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j));

Hard Decision Le={ei,ej}={not(ai),not(aj)}; and

Hard Decision Le′={ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)).

Once the pivot value (m) is calculated, data pre-processing circuit 260compares the pivot value to a threshold value. In some cases, thethreshold value is programmable, and in other cases it is fixed. In oneparticular embodiment of the present invention, the threshold values isset at 0.75. Where the pivot value is greater than the threshold value,then data pre-processing circuit 260 asserts a pre-processed output 261in accordance with the following equation:

Output 261=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)].

Alternatively, where the pivot value is less than or equal to thethreshold value, then data pre-processing circuit 260 asserts apre-processed output 261 in accordance with the following equation:

Output 261=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei′),(−1)^(ej′)].

Pre-processing output 261 is provided from data pre-processing circuit260 to binary short media defect detector circuit 270. Binary mediadefect detector circuit 270 may be any defect detector circuit known inthe art that operates on a series of binary data to yield the locationof a potential media defect in relation to the series of received data.In one particular embodiment of the present invention, binary mediadefect detector circuit 270 may be implemented similar to that disclosedin U.S. patent application Ser. No. 13/088,119 entitled “Systems andMethods for Short Media Defect Detection”, and filed Apr. 15, 2011 byZhang et al. The entirety of the aforementioned reference isincorporated herein by reference for all purposes.

When binary media defect detector circuit 270 identifies a media defectit asserts a defect indicator 271 to a scaling circuit 220. Selectivescaling circuit 220 delays detected output 211 to align it with defectindicator 271. Where defect indicator 271 is asserted, selective scalingcircuit 220 applies a symbol by symbol scaling to each symbol indetected output 211 that corresponds to defect indicator 271. Thisscaling operates to modify soft data associated with the effectedsymbols to reduce the probability that the symbol is considered properlyfound. By doing this, the likelihood that an effected symbol negativelyimpacts processing of the data set is reduced and the likelihood thatthe symbol will be modified by later processing is increased. Selectivescaling circuit 220 provides a scaled output 221 to a data decodercircuit 230.

Data decoder circuit 230 applies a data decode algorithm to scaledoutput 221 to yield a decoded output that includes soft decoded output232. In some embodiments of the present invention, data decoder circuit230 is a low density parity check decoder circuit as are known in theart. Where the decoded output converges (i.e., yields the original dataset as indicated by the lack of remaining errors), it is provided as adata output 231.

Turning to FIG. 3, a flow diagram 300 shows a method in accordance withsome embodiments of the present invention for data processing includingshort media defect detection. Following flow diagram 300, it isdetermined whether a data detector circuit is available to process anewly received data set or a data set that has already been subject toone or more prior global iterations (block 310). As used herein, thephrase “global iteration” is used in its broadest sense to meanapplication of both a data detection algorithm and a data decodealgorithm. Also, as used herein, the phrase “local iteration” is used inits broadest sense to mean an application of the data decode algorithm.In some instances of the present invention, one or more local iterationsmay be performed for each global iteration.

Where a data detector circuit is available (block 310), a processingdata input is accessed and it is determined whether a decoded outputcorresponding to the accessed processing data input exists (block 320).Such a decoded output is available as a result from a preceding globaliteration applied to the same processing data input. The processing datainput may be, for example, derived from a storage medium. Where acorresponding decoded output is not available (block 320), a datadetection algorithm is applied to the processing data input to yield adetected output (block 325). The data detection algorithm may be, but isnot limited to, a Viterbi data detection algorithm or a maximum aposteriori data detection algorithm as are known in the art. Based uponthe disclosure provided herein, one of ordinary skill in the art willrecognize a variety of data detection algorithms that may be used inrelation to different embodiments of the present invention.

Alternatively, where a corresponding decoded output is available (block320) it is accessed (block 315) and a data detection algorithm isapplied to the processing data input guided by the corresponding decodedoutput to yield a detected output (block 330). Such a correspondingdecoded output is available for the second or later global iterationsfor a given processing data input. A symbol data pre-processing isapplied to the detected output to yield a pre-processed detected output(block 335). This includes: (1) calculating a pivot point (m), and (2)based on the pivot point generating the pre-processed detected output.In particular, the pivot point (m) is calculated in accordance with thefollowing equation:

$m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}$

where i, j indicate a particular element of a given symbol. For two bitsymbols, i goes from 0 to 1 and j goes from 0 to 1. It should be notedthat while this embodiment is described in relation to two bit symbolsthat it may be used in relation to symbols with three or more bits. Forthe case of two bit symbols, “Sa” represents a soft data element of thedetected output (La), and “Se” represents a soft data element of thecorresponding decoded output (Le), and the detected output (La) and thedecoded output (Le) are defined as follow:

La=[Soft Data_(—) a ₀₀,Soft Data_(—) a ₀₁,Soft Data_(—) a ₁₀,SoftData_(—) a ₁₁]; and

Le=[Soft Data_(—) e ₀₀,Soft Data_(—) e ₀₁,Soft Data_(—) e ₁₀,SoftData_(—) e ₁₁].

In some cases, Soft Data_a_(i,j) and Soft Data_e_(i,j) are loglikelihood ratio (LLR) data. In such a case, the hard decision of eachsymbol of the detected output (La) and the hard decision of each symbolof the corresponding decoded output (Le) are described as follows:

Hard Decision La={ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j));

Hard Decision Le={ei,ej}={not(ai),not(aj)}; and

Hard Decision Le′={ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)).

Once the pivot value (m) is calculated, it is compared with a thresholdvalue and a pre-processed detected output is generated based upon thecomparison in accordance with the following equations:

Output=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)],

for m>Threshold; and

Output=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei)′,(−1)^(ej)′],

for m<=Threshold.

This output is provided as the pre-processed detected output.

A binary short media defect detection is applied to the pre-processeddetected output to determine whether a media defect is likely, and if soto provide a media defect location set (block 340). Such a media defectlocation set indicates which data in the processing data set correspondsto the likely media defect. The binary short media defect detection maybe any media defect detection process known in the art. In oneparticular embodiment of the present invention, the binary media defectdetection processed may be done similar to that disclosed in U.S. patentapplication Ser. No. 13/088,119 entitled “Systems and Methods for ShortMedia Defect Detection”, and filed Apr. 15, 2011 by Zhang et al. Theentirety of the aforementioned reference was previously incorporatedherein by reference for all purposes.

Symbols of the detected output corresponding to the media defectlocation set are scaled to update the detected output (block 345). Thisscaling operates to modify soft data associated with the effectedsymbols to reduce the probability that the symbol is considered properlyfound. By doing this, the likelihood that an effected symbol negativelyimpacts processing of the data set is reduced and the likelihood thatthe symbol will be modified by later processing is increased.

All local iterations of a data decode algorithm are then applied to thedetected output guided by a previous decoded output where available(block 350). This process generates an updated decoded output that maybe used during subsequent global iterations where it does not converge(i.e., have no remaining unsatisfied checks). In some embodiments of thepresent invention, the data decode algorithm is a low density paritycheck algorithm as is known in the art. It is determined whether thedata decode algorithm converged (block 355). Where the data decodealgorithm converged (block 355), the decoded output is provided as anoutput codeword, and the next processing data input is selected forprocessing (block 370). Alternatively, where the data decode algorithmfailed to converge (block 355), it is determined whether another globaliteration is allowed (block 360). Where another global iteration is notallowed (block 360), a failure is indicated (block 361) and the decodedoutput is provided as an output codeword, and the next processing datainput is selected for processing (block 370). In contrast, where anotherglobal iteration is allowed (block 360), a subsequent location iterationis applied to the same processing data input guided by the results ofthe preceding global iteration.

Turning to FIG. 4, another data processing circuit 400 including a shortdefect detector circuit 460 (shown in dashed lines) is shown inaccordance with various embodiments of the present invention. Dataprocessing circuit 400 includes an analog front end circuit 410 thatreceives an analog signal 405. Analog front end circuit 410 processesanalog signal 405 and provides a processed analog signal 412 to ananalog to digital converter circuit 414. Analog front end circuit 410may include, but is not limited to, an analog filter and an amplifiercircuit as are known in the art. Based upon the disclosure providedherein, one of ordinary skill in the art will recognize a variety ofcircuitry that may be included as part of analog front end circuit 410.In some cases, analog signal 405 is derived from a read/write headassembly (not shown) that is disposed in relation to a storage medium(not shown). Based upon the disclosure provided herein, one of ordinaryskill in the art will recognize a variety of media from which analogsignal 405 may be derived.

Analog to digital converter circuit 414 converts processed analog signal412 into a corresponding series of digital samples 416. Analog todigital converter circuit 414 may be any circuit known in the art thatis capable of producing digital samples corresponding to an analog inputsignal. Based upon the disclosure provided herein, one of ordinary skillin the art will recognize a variety of analog to digital convertercircuits that may be used in relation to different embodiments of thepresent invention. Digital samples 416 are provided to an equalizercircuit 420. Equalizer circuit 420 applies an equalization algorithm todigital samples 416 to yield an equalized output 425. In someembodiments of the present invention, equalizer circuit 420 is a digitalfinite impulse response filter circuit as are known in the art. It maybe possible that equalized output 425 may be received directly from astorage device in, for example, a solid state storage system. In suchcases, analog front end circuit 410, analog to digital converter circuit414 and equalizer circuit 420 may be eliminated where the data isreceived as a digital data input.

Equalized output 425 is stored to an input buffer 453 that includessufficient memory to maintain one or more codewords until processing ofthat codeword is completed through an iterative data processing circuit499 (outlined by dashed lines) including, where warranted, multipleglobal iterations (passes through both a data detector circuit 430 and adata decoder circuit 370) and/or local iterations (passes through datadecoder circuit 470 during a given global iteration). An output 457 isprovided to a data detector circuit 430

Data detector circuit 430 may be a single data detector circuit or maybe two or more data detector circuits operating in parallel on differentcodewords (i.e., data sets). Whether it is a single data detectorcircuit or a number of data detector circuits operating in parallel,data detector circuit 430 is operable to apply a data detectionalgorithm to a received codeword or data set. In some embodiments of thepresent invention, data detector circuit 430 is a Viterbi algorithm datadetector circuit as are known in the art. In other embodiments of thepresent invention, data detector circuit 430 is a maximum a posterioridata detector circuit as are known in the art. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of data detector circuits that may be used in relation todifferent embodiments of the present invention. In some cases, one datadetector circuit included in data detector circuit 430 is used to applythe data detection algorithm to the received codeword for a first globaliteration applied to the received codeword, and another data detectorcircuit included in data detector circuit 430 is operable apply the datadetection algorithm to the received codeword guided by a decoded outputaccessed from a central memory circuit 450 on subsequent globaliterations.

Upon completion of application of the data detection algorithm to thereceived codeword (i.e., processing data input) on the first globaliteration, data detector circuit 430 provides a detector output 433.Detector output 433 includes soft data (La). As used herein, the phrase“soft data” is used in its broadest sense to mean reliability data witheach instance of the reliability data indicating a likelihood that acorresponding bit position or symbol has been correctly detected. Insome embodiments of the present invention, the soft data or reliabilitydata is log likelihood ratio data as is known in the art. Detectedoutput 433 is provided to a local interleaver circuit 442 via a scalingcircuit 441. Scaling circuit 441 operates to scale one or more symbolsin detected output 433 corresponding to a media defect as indicated by adefect indicator 461. This scaling operates to modify soft dataassociated with the effected symbols of detector output 433 to reducethe probability that the symbol is considered properly found. By doingthis, the likelihood that an effected symbol negatively impactsprocessing of the codeword is reduced and the likelihood that the symbolwill be modified by later processing is increased. Scaling circuit 441provides a scaled detected output 443 to local interleaver circuit 442.Where no defects are indicated by defect indicator 461, scaled detectedoutput 443 is the same as detected output 433.

Local interleaver circuit 442 is operable to shuffle sub-portions (i.e.,local chunks) of the data set included as detected output and providesan interleaved codeword 446 that is stored to central memory circuit450. Interleaver circuit 442 may be any circuit known in the art that iscapable of shuffling data sets to yield a re-arranged data set.Interleaved codeword 446 is stored to central memory circuit 450.

Once data decoder circuit 470 is available, a previously storedinterleaved codeword 446 is accessed from central memory circuit 450 asa stored codeword 486 and globally interleaved by a globalinterleaver/de-interleaver circuit 484. Globalinterleaver/De-interleaver circuit 484 may be any circuit known in theart that is capable of globally rearranging codewords. Globalinterleaver/De-interleaver circuit 484 provides a decoder input 452 intodata decoder circuit 470. In some embodiments of the present invention,data decoder circuit 470 is a low density parity check decoder circuitas are known in the art. Application of the data decode algorithm bydata decoder circuit 470 yield a decoded output 474. In cases where thedecoded output 474 fails to converge (i.e., failed to yield theoriginally written data set) and another local iteration (i.e., anotherpass through data decoder circuit 470) is desired, data decoder circuit470 re-applies the data decode algorithm to decoder input 452 guided bydecoded output 474. This continues until either a maximum number oflocal iterations is exceeded or decoded output 474 converges.

Where decoded output 474 fails to converge and a number of localiterations through data decoder circuit 470 exceeds a threshold, theresulting decoded output is provided as a decoded output 454 back tocentral memory circuit 450 where it is stored awaiting another globaliteration through a data detector circuit included in data detectorcircuit 430. Prior to storage of decoded output 454 to central memorycircuit 450, decoded output 454 is globally de-interleaved to yield aglobally de-interleaved output 488 that is stored to central memorycircuit 450. The global de-interleaving reverses the global interleavingearlier applied to stored codeword 486 to yield decoder input 452. Whena data detector circuit included in data detector circuit 430 becomesavailable, a previously stored de-interleaved output 488 accessed fromcentral memory circuit 450 and locally de-interleaved by ade-interleaver circuit 444. De-interleaver circuit 444 re-arrangesdecoder output 448 to reverse the shuffling originally performed byinterleaver circuit 442. A resulting de-interleaved output 497 isprovided to data detector circuit 430 where it is used to guidesubsequent detection of a corresponding data set previously received asequalized output 425.

Alternatively, where the decoded output converges (i.e., yields theoriginally written data set), the resulting decoded output is providedas an output codeword 472 to a de-interleaver circuit 480.De-interleaver circuit 480 rearranges the data to reverse both theglobal and local interleaving applied to the data to yield ade-interleaved output 482. De-interleaved output 482 is provided to ahard decision output circuit 490. Hard decision output circuit 490 isoperable to re-order data sets that may complete out of order back intotheir original order. Ultimately, hard decision output circuit 490provides the converged codeword as a data output to a recipient device(not shown).

Iterative data processing circuit 499 includes short defect detectorcircuit 460 that is operable to identify one or more likely defectiveregions on a medium from which analog input 405 is derived. Suchdefective regions are indicated by defect indicator 461 provided toscaling circuit 441. Short defect detector circuit 460 includes datapre-processing circuit 462 and a binary short media defect detectorcircuit 464.

De-interleaved output (Le) 497 (i.e., a version of decoded output 454)and detected output (La) 433 are provided to data pre-processing circuit462 that is operable to modify a symbol based information set into abinary based information set. In particular, a pivot value (m) iscomputed in accordance with the following equation:

${m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}},$

where i, j indicate a particular element of a given symbol. For two bitsymbols, i goes from 0 to 1 and j goes from 0 to 1. It should be notedthat while this embodiment is described in relation to two bit symbolsthat it may be used in relation to symbols with three or more bits. Forthe case of two bit symbols, “Sa” represents a soft data element ofdetected output (La) 433, and “Se” represents a soft data element ofde-interleaved output (Le) 497, and detected output (La) 433 andde-interleaved output (Le) 497 are defined as follow:

La=[Soft Data_(—) a ₀₀,Soft Data_(—) a ₀₁,Soft Data_(—) a ₁₀,SoftData_(—) a ₁₁]; and

Le=[Soft Data_(—) e ₀₀,Soft Data_(—) e ₀₁,Soft Data_(—) e ₁₀,SoftData_(—) e ₁₁].

In some cases, Soft Data_a_(i,j) and Soft Data_e_(i,j) are loglikelihood ratio (LLR) data. In such a case, the hard decision of eachsymbol of detected output (La) 433 and the hard decision of each symbolof de-interleaved output (Le) 497 are described as follows:

Hard Decision La={ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j));

Hard Decision Le={ei,ej}={not(ai),not(aj)}; and

Hard Decision Le′={ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)).

Once the pivot value (m) is calculated, data pre-processing circuit 462compares the pivot value to a threshold value. In some cases, thethreshold value is programmable, and in other cases it is fixed. In oneparticular embodiment of the present invention, the threshold values isset at 0.75. Where the pivot value is greater than the threshold value,then data pre-processing circuit 462 asserts a pre-processed output 463in accordance with the following equation:

Output 463=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)].

Alternatively, where the pivot value is less than or equal to thethreshold value, then data pre-processing circuit 462 asserts apre-processed output 463 in accordance with the following equation:

Output 463=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei′),(−1)^(ej′)].

Pre-processing output 463 is provided from data pre-processing circuit462 to binary short media defect detector circuit 464. Binary mediadefect detector circuit 464 may be any defect detector circuit known inthe art that operates on a series of binary data to yield the locationof a potential media defect in relation to the series of received data.In one particular embodiment of the present invention, binary mediadefect detector circuit 464 may be implemented similar to that disclosedin U.S. patent application Ser. No. 13/088,119 entitled “Systems andMethods for Short Media Defect Detection”, and filed Apr. 15, 2011 byZhang et al. The entirety of the aforementioned reference was previouslyincorporated herein by reference for all purposes.

When binary media defect detector circuit 464 identifies a media defectit asserts a defect indicator 461 to scaling circuit 441. Scalingcircuit 441 delays detected output 433 to align it with defect indicator461. Where defect indicator 461 is asserted, scaling circuit 441 appliesa symbol by symbol scaling to each symbol in detected output 433 thatcorresponds to defect indicator 461.

Turning to FIGS. 5 a-5 b, flow diagrams 500, 501 show a method inaccordance with one or more embodiments of the present invention fordata processing including short media defect detection. Following flowdiagram 500 of FIG. 5 a, it is determined whether a decoded output isready in the central memory to guide re-application of a data detectionalgorithm to a data processing input, or if a new data processing inputis ready for processing (block 505). It is then determined whether adata detector circuit is available (block 510). Where a data detectorcircuit is available (block 510), the next processing data input isaccessed and it is determined whether a decoded output corresponding tothe detected output is available from the central memory (block 515).The decoded output is available for the second or later globaliterations.

Where a corresponding decoded output is not available (block 515), adata detection algorithm is applied to the processing data input toyield a detected output (block 520). The data detection algorithm maybe, but is not limited to, a Viterbi data detection algorithm or amaximum a posteriori data detection algorithm as are known in the art.Based upon the disclosure provided herein, one of ordinary skill in theart will recognize a variety of data detection algorithms that may beused in relation to different embodiments of the present invention.

Alternatively, where a corresponding decoded output is available (block515) it is accessed (block 525) and a data detection algorithm isapplied to the processing data input guided by the corresponding decodedoutput to yield a detected output (block 530). Such a correspondingdecoded output is available for the second or later global iterationsfor a given processing data input. A symbol data pre-processing isapplied to the detected output to yield a pre-processed detected output(block 535). This includes: (1) calculating a pivot point (m), and (2)based on the pivot point generating the pre-processed detected output.In particular, the pivot point (m) is calculated in accordance with thefollowing equation:

$m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}$

where i, j indicate a particular element of a given symbol. For two bitsymbols, i goes from 0 to 1 and j goes from 0 to 1. It should be notedthat while this embodiment is described in relation to two bit symbolsthat it may be used in relation to symbols with three or more bits. Forthe case of two bit symbols, “Sa” represents a soft data element of thedetected output (La), and “Se” represents a soft data element of thecorresponding decoded output (Le), and the detected output (La) and thedecoded output (Le) are defined as follow:

La=[Soft Data_(—) a ₀₀,Soft Data_(—) a ₀₁,Soft Data_(—) a ₁₀,SoftData_(—) a ₁₁]; and

Le=[Soft Data_(—) e ₀₀,Soft Data_(—) e ₀₁,Soft Data_(—) e ₁₀,SoftData_(—) e ₁₁].

In some cases, Soft Data_a_(i,j) and Soft Data_e_(i,j) are loglikelihood ratio (LLR) data. In such a case, the hard decision of eachsymbol of the detected output (La) and the hard decision of each symbolof the corresponding decoded output (Le) are described as follows:

Hard Decision La={ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j));

Hard Decision Le={ei,ej}={not(ai),not(aj)}; and

Hard Decision Le′={ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)).

Once the pivot value (m) is calculated, it is compared with a thresholdvalue and a pre-processed detected output is generated based upon thecomparison in accordance with the following equations:

Output=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)],

for m>Threshold; and

Output=[(−1)^(ai),(−1)^(aj)]and[(−1)^(ei)′,(−1)^(ej)′],

for m<=Threshold.

This output is provided as the pre-processed detected output.

A binary short media defect detection is applied to the pre-processeddetected output to determine whether a media defect is likely, and if soto provide a media defect location set (block 540). Such a media defectlocation set indicates which data in the processing data set correspondsto the likely media defect. The binary short media defect detection maybe any media defect detection process known in the art. In oneparticular embodiment of the present invention, the binary media defectdetection processed may be done similar to that disclosed in U.S. patentapplication Ser. No. 13/088,119 entitled “Systems and Methods for ShortMedia Defect Detection”, and filed Apr. 15, 2011 by Zhang et al. Theentirety of the aforementioned reference was previously incorporatedherein by reference for all purposes.

Symbols of the detected output corresponding to the media defectlocation set are scaled to update the detected output (block 545). Thisscaling operates to modify soft data associated with the effectedsymbols to reduce the probability that the symbol is considered properlyfound. By doing this, the likelihood that an effected symbol negativelyimpacts processing of the data set is reduced and the likelihood thatthe symbol will be modified by later processing is increased.

All local iterations of a data decode algorithm are then applied to thedetected output guided by a previous decoded output where available(block 550). This process generates an updated decoded output that maybe used during subsequent global iterations where it does not converge(i.e., have no remaining unsatisfied checks). A derivative of theresulting detected output (block 520, 545) is stored to the centralmemory to await processing by a data decoder circuit (block 550). Insome cases, the derivative of the detected output is an interleaved orshuffled version of the detected output.

Turning to FIG. 5 b and following flow diagram 501, in parallel to thepreviously described data detection process, it is determined whether adata decoder circuit is available (block 506). The data decoder circuitmay be, for example, a low density data decoder circuit as are known inthe art. Where the data decoder circuit is available (block 506), apreviously stored derivative of a detected output is accessed from thecentral memory and used as a received codeword (block 511). A datadecode algorithm is applied to the received codeword to yield a decodedoutput (block 516). It is then determined whether the decoded outputconverged (e.g., resulted in the originally written data as indicated bythe lack of remaining unsatisfied checks) (block 521). Where the decodedoutput converged (block 521), the converged codeword is provided as adecoded output (block 526).

Alternatively, where the decoded output failed to converge (e.g., errorsremain) (block 521), it is determined whether another local iteration isdesired (block 531). In some cases, as a default seven local iterationsare allowed per each global iteration. Based upon the disclosureprovided herein, one of ordinary skill in the art will recognize anotherdefault number of local iterations that may be used in relation todifferent embodiments of the present invention. Where another localiteration is desired (block 531), the data decode algorithm isre-applied using the current decoded output as a guide (block 516).

Alternatively, where another local iteration is not desired (block 531),it is determined whether another global iteration is allowed (block536). As a default, another global iteration is allowed where there issufficient available space in the central memory and an output memoryreordering queue to allow another pass through processing the currentlyprocessing codeword. The amount of available space in the central memoryand an output memory reordering queue is a function of how manyiterations are being used by concurrently processing codewords toconverge. For more detail on the output queue time limitation see, forexample, U.S. patent application Ser. No. 12/114,462 entitled “Systemsand Methods for Queue Based Data Detection and Decoding”, and filed May8, 2008 by Yang et al. The entirety of the aforementioned reference isincorporated herein by reference for all purposes. Thus, the amount oftime that a codeword may continue processing through global iterationsis a function of the availability of central memory and an output memoryreordering queue. By limiting the number of global iterations that maybe performed, the amount of time a codeword may continue processingthrough global iterations can be reduced.

Where another global iteration is allowed (block 536), a derivative ofthe decoded output is stored to the central memory (block 546). Thederivative of the decoded output being stored to the central memorytriggers the data set ready query of block 505 to begin the datadetection process. Alternatively, where another global iteration is notallowed (block 536), a failure to converge is indicated (block 541), andthe current decoded output is provided (block 526).

It should be noted that the various blocks discussed in the aboveapplication may be implemented in integrated circuits along with otherfunctionality. Such integrated circuits may include all of the functionsof a given block, system or circuit, or only a subset of the block,system or circuit. Further, elements of the blocks, systems or circuitsmay be implemented across multiple integrated circuits. Such integratedcircuits may be any type of integrated circuit known in the artincluding, but are not limited to, a monolithic integrated circuit, aflip chip integrated circuit, a multichip module integrated circuit,and/or a mixed signal integrated circuit. It should also be noted thatvarious functions of the blocks, systems or circuits discussed hereinmay be implemented in either software or firmware. In some such cases,the entire system, block or circuit may be implemented using itssoftware or firmware equivalent. In other cases, the one part of a givensystem, block or circuit may be implemented in software or firmware,while other parts are implemented in hardware.

In conclusion, the invention provides novel systems, devices, methodsand arrangements for performing defect detection. While detaileddescriptions of one or more embodiments of the invention have been givenabove, various alternatives, modifications, and equivalents will beapparent to those skilled in the art without varying from the spirit ofthe invention. For example, one or more embodiments of the presentinvention may be applied to various data storage systems and digitalcommunication systems, such as, for example, tape recording systems,optical disk drives, wireless systems, and digital subscriber linesystems. Therefore, the above description should not be taken aslimiting the scope of the invention, which is defined by the appendedclaims.

What is claimed is:
 1. A data processing system, the data processing system comprising: a data detector circuit operable to apply a data detection algorithm to a symbol based data set guided by a decoded output to yield a symbol based detected output; a defect detector circuit including: a data pre-processing circuit operable to pre-process the symbol based detected output to yield a pre-processed output; and a binary data detection circuit operable to provide a defect indicator corresponding to a probable defect identified based on the pre-processed output; and a data decoder circuit operable to apply a data decode algorithm to a decoder input derived from the detected output modified based on the defect indicator to update the decoded output.
 2. The data processing system of claim 1, wherein the symbol based data set is a series of multi-bit symbols.
 3. The data processing system of claim 2, wherein the multi-bit symbols are two bit symbols.
 4. The data processing system of claim 2, wherein the data pre-processing circuit is further operable to: calculate an input value based upon a combination of the detected output and the decoded output; and compare the input value with a threshold value.
 5. The data processing system of claim 4, wherein the threshold value is programmable.
 6. The data processing system of claim 4, wherein the input value is calculated in accordance with the following equation: ${m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}},$ wherein i, j indicate a particular element of one of the series of multi-bit symbols, wherein ei, ej indicate a particular element of the one of the series of multi-bit symbols, wherein ai, aj indicate a particular element of the one of the series of multi-bit symbols, wherein Sa_(i,j) represents a soft data element of the detected output, wherein Sa_(ai,aj) represents a soft data element of the detected output, wherein Se_(i,j) represents a soft data element of the decoded output, and wherein Se_(ei,ej) represents a soft data element of the decoded output.
 7. The data processing system of claim 4, wherein the pre-processed output is calculated in accordance with the following equation: [(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)], where the input value is greater than the threshold; and [(−1)^(ai),(−1)^(aj)]and[(−1)^(ei)′,(−1)^(ej)′], where the input value is less than the threshold, and wherein ei, ej indicate a particular element of one of the series of multi-bit symbols, wherein the ei′, ej′ indicate a particular element of the one of the series of multi-bit symbols, and wherein ai, aj indicate a particular element of the one of the series of multi-bit symbols.
 8. The data processing system of claim 7, wherein ai, aj, ei, ej, ei′, and ej′ are defined in accordance with the following equations: {ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j)); {ei,ej}={not(ai),not(aj)}; and {ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)); and wherein Soft Data_a_(i,j) represents a soft data element of the detected output, and wherein Soft Data_e_(i,j) represents a soft data element of the decoded output.
 9. The data processing system of claim 1, wherein the system is implemented as an integrated circuit.
 10. The data processing system of claim 1, wherein the system is implemented as part of a storage device.
 11. The data processing system of claim 1, wherein the data decoder circuit is a low density parity check decoder circuit.
 12. The data processing system of claim 1, wherein the data detector circuit is selected from a group consisting of: a Viterbi algorithm data detector circuit, and a maximum a posteriori data detector circuit.
 13. A method for data processing, the method comprising: applying a data detection algorithm by a data detector circuit to a symbol based data set guided by a decoded output to yield a symbol based detected output; pre-processing the symbol based detected output to yield a pre-processed output; providing a defect indicator corresponding to a probable defect identified based on the pre-processed output; and applying a data decode algorithm to a decoder input derived from the detected output modified based on the defect indicator to update the decoded output.
 14. The method of claim 14, wherein the symbol based data set is a series of multi-bit symbols, and wherein pre-processing the symbol based detected output includes: calculating an input value based upon a combination of the detected output and the decoded output; and comparing the input value with a threshold value.
 15. The method of claim 14, wherein the input value is calculated in accordance with the following equation: ${m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}},$ wherein i, j indicate a particular element of one of the series of multi-bit symbols, wherein ei, ej indicate a particular element of the one of the series of multi-bit symbols, wherein ai, aj indicate a particular element of the one of the series of multi-bit symbols, wherein Sa_(i,j) represents a soft data element of the detected output, wherein Sa_(ai,aj) represents a soft data element of the detected output, wherein Se_(i,j) represents a soft data element of the decoded output, and wherein Se_(ei,ej) represents a soft data element of the decoded output.
 16. The method of claim 14, wherein the pre-processed output is calculated in accordance with the following equation: [(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)], where the input value is greater than the threshold; and [(−1)^(ai),(−1)^(aj)]and[(−1)^(ei)′,(−1)^(ej)′], where the input value is less than the threshold, and wherein ei, ej indicate a particular element of one of the series of multi-bit symbols, wherein the ei′, ej′ indicate a particular element of the one of the series of multi-bit symbols, and wherein ai, aj indicate a particular element of the one of the series of multi-bit symbols; and wherein ai, aj, ei, ej, ei′, and ej′ are defined in accordance with the following equations: {ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j)); {ei,ej}={not(ai),not(aj)}; and {ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)); and wherein Soft Data_a_(i,j) represents a soft data element of the detected output, and wherein Soft Data_e_(i,j) represents a soft data element of the decoded output.
 17. A storage device, the storage device comprising: a storage medium; a read/write head assembly operable to sense information from the storage medium and to provide a corresponding continuous signal; an analog to digital converter circuit operable to sample the continuous signal synchronous to a sampling clock to yield a set of digital samples; an equalizer circuit operable to equalize the set of digital samples and to provide a corresponding symbol based equalized output; a data detector circuit operable to apply a data detection algorithm to a symbol based equalized output guided by a decoded output to yield a symbol based detected output; a defect detector circuit including: a data pre-processing circuit operable to pre-process the symbol based detected output to yield a pre-processed output; and a binary data detection circuit operable to provide a defect indicator corresponding to a probable defect identified based on the pre-processed output; and a data decoder circuit operable to apply a data decode algorithm to a decoder input derived from the detected output modified based on the defect indicator to update the decoded output.
 18. The storage device of claim 17, wherein the symbol based data set is a series of multi-bit symbols, and wherein the data pre-processing circuit is further operable to: calculate an input value based upon a combination of the detected output and the decoded output; and compare the input value with a threshold value.
 19. The storage device of claim 17, wherein the input value is calculated in accordance with the following equation: ${m = \frac{{\sum\limits_{i,j}\; \left( {{Sa}_{i,j} - {2*{Sa}_{{ai},{aj}}}} \right)} + {\sum\limits_{i,j}\; \left( {{Se}_{i,j} - {2*{Se}_{{ei},{ej}}}} \right)}}{{\sum\limits_{i,j}\; {Sa}_{i,j}} + {Se}_{i,j}}},$ wherein i, j indicate a particular element of one of the series of multi-bit symbols, wherein ei, ej indicate a particular element of the one of the series of multi-bit symbols, wherein ai, aj indicate a particular element of the one of the series of multi-bit symbols, wherein Sa_(i,j) represents a soft data element of the detected output, wherein Sa_(ai,aj) represents a soft data element of the detected output, wherein Se_(i,j) represents a soft data element of the decoded output, and wherein Se_(ei,ej) represents a soft data element of the decoded output.
 20. The storage device of claim 18, wherein the pre-processed output is calculated in accordance with the following equation: [(−1)^(ai),(−1)^(aj)]and[(−1)^(ei),(−1)^(ej)], where the input value is greater than the threshold; and [(−1)^(ai),(−1)^(aj)]and[(−1)^(ei)′,(−1)^(ej)′], where the input value is less than the threshold, and wherein ei, ej indicate a particular element of one of the series of multi-bit symbols, wherein the ei′, ej′ indicate a particular element of the one of the series of multi-bit symbols, and wherein ai, aj indicate a particular element of the one of the series of multi-bit symbols.
 21. The storage device of claim 20, wherein ai, aj, ei, ej, ei′, and ej′ are defined in accordance with the following equations: {ai,aj}=arg max_(i,j)(Soft Data_(—) a _(i,j)); {ei,ej}={not(ai),not(aj)}; and {ei′,ej′}=arg max_(i,j)(Soft Data_(—) e _(i,j)); and wherein Soft Data_a_(i,j) represents a soft data element of the detected output, and wherein Soft Data_e_(i,j) represents a soft data element of the decoded output. 